If three dice are thrown at a time, then the probability of getting the sum of the numbers on them as a prime number is

Three companies $C_1, C_2, C_3$ produce car tyres. A car manufacturing company buys $40 \%$ of its requirement from $C_1, 35 \%$ from $C_2$ and $25 \%$ from $C_3$. The company knows that $2 \%$ of the tyres supplied by $C_1, 3 \%$ by $C_2$ and $4 \%$ by $C_3$ are defective. If a tyre chosen random from the consignment received is found defective then, the probability that it was supplied by $C_2$ is

The probability distribution of a random variable $X$ is given below. Then, the standard deviation of $X$ is

$$ \begin{array}{llllll} \hline \boldsymbol{X}=\boldsymbol{x}_1 & 2 & 3 & 5 & 7 & 12 \\ \hline \boldsymbol{P}\left(\boldsymbol{X}=\boldsymbol{x}_1\right) & 3 k & k & k & 2 k & k \\ \hline \end{array} $$

If the mean and variance of a binomial distribution are $\frac{4}{3}$ and $\frac{10}{9}$ respectively, then $P(X \geq 6)=$